Stage level,volume and time‐frequency information content of Lake Tana using stochastic and wavelet analysis methods

Lake Tana is the largest fresh water body situated in the north‐western highlands of Ethiopia. In addition to its ecological services, it serves for local transport, electric power generation, fishing, recreational purposes, and source of dry season irrigation water supply. Evidence shows that the lake has dried at least once at about 15,000–17,000 before present owing to a combination of high evaporation and low precipitation events. Past attempts to understand and simulate historical fluctuation of Lake Tana based on simplistic water balance approach of inflow, outflow, and storage have failed to capture well‐known events of drawdown and rise of the lake that have happened in the last 44 years. This study tested different stochastic methods of lake level and volume simulation for supporting Lake Tana operational planning decision support. Three stochastic methods (perturbations approach, Monte Carlo methods, and wavelet analysis) were employed for lake level and volume simulation, and the results were compared with the stage level measurements. Forty‐four years of daily, monthly, and mean annual lake level data have shown a Gaussian variation with goodness of fit at 0.01 significant levels of the Kolmogorov–Smirnov test. The stochastic simulations predicted the lake stage level of the 1972, 1984, and 2002/2003 historical droughts 99% of the time. The information content (frequency) of fluctuation of Lake Tana for various periods was resolved using Wigner's Time‐Frequency Decomposition method. The wavelet analysis agreed with the perturbations and Monte Carlo simulations resolving the time (1970s, 1980s, and 2000s) in which low frequency and high spectral power fluctuation has occurred. The Monte Carlo method has shown its superiority for risk analysis over perturbation and deterministic method whereas wavelet analysis reconstructed historical record of lake stage level at daily and monthly time scales. Copyright © 2012 John Wiley & Sons, Ltd.     

Simulating the effects of spatial configurations of agricultural ditch drainage networks on surface runoff from agricultural catchments

The study of runoff is a crucial issue because it is closely related to flooding, water quality and erosion. In cultivated catchments, agricultural ditch drainage networks are known to influence runoff. As anthropogenic elements, agricultural ditch drainage networks can therefore be altered to better manage surface runoff in cultivated catchments. However, the relationship between the spatial configuration, i.e. the density and the topology, of agricultural ditch drainage networks and surface runoff in cultivated catchments is not understood. We studied this relationship by using a random network simulator that was coupled to a distributed hydrological model. The simulations explored a large variety of spatial configurations corresponding to a thousand stochastic agricultural ditch drainage networks on a 6.4 km² Mediterranean cultivated catchment. Next, several distributed hydrological functions were used to compute water flow paths and runoff for each simulation. The results showed that (i) denser networks increased the drained volume and the peak discharge and decreased hillslopes runoff, (ii) greater network density did not affect the surface runoff any further above a given network density, (iii) the correlation between network density and runoff was weaker for small subcatchments (< 2 km²) where the variability in the drained area that resulted from changes in agricultural ditch drainage networks increased the variability of runoff and (iv) the actual agricultural ditch drainage network appeared to be well optimized for managing runoff as compared with the simulated networks. Finally, our results highlighted the role of agricultural ditch drainage networks in intercepting and decreasing overland flow on hillslopes and increasing runoff in drainage networks. Copyright © 2011 John Wiley & Sons, Ltd.     

Generation of correlated properties in heterogeneous porous media

The spatial distribution of rock properties in porous media, such as permeability and porosity, often is strongly variable. Therefore, these properties usefully may be considered as a random field. However, this variability is correlated frequently on length scales comparable to geological lengths (for example, scales of sand bodies or facies). To solve various engineering problems (for example, in the oil recovery process) numerical models of a porous medium often are used. A need exists then to understand correlated random fields and to generate them over discretized numerical grids. The paper describes the general mathematical methods required to do this, with one particular method (the nearest neighbor model) described in detail. How parameters of the mathematical model may be related to rock property statistics for the nearest neighbor model is shown. The method is described in detail in one, two, and three dimensions. Examples are given of how model parameters may be determined from real data.     

Simulation of the time-space evolution of an extratropical cyclonic precipitation field over USA

The time-space evolution of an extratropical cyclonic precipitation field over U S A is simulated in a stochastic setting as outlined in Kavvas et al. (1988). The birth of a cyclonic storm is characterized by the simultaneous birth of a cyclone center and births of subsynoptic precipitation areas (SPA) at preferred locations around the cyclone center. The precipitation cores and cells which are used as the fundamental building blocks of the SPAs are approximated by circular precipitation areas (CPA) of different sizes. The time space evolution of the precipitation field after the birth is governed by (1) the movement of the synoptic cyclone described by the cyclone center trajectory, (2) independent nonidentically distributed random velocities of the individual CPAs relative to the cyclone center, (3) the births of new CPAs in time and space relative to the cyclone center, (4) the independent evolution in time of the individual spatially uniform intensities of the existing CPAs, (5) the expansion and shrinkage of the existing CPAs in the course of movement and (6) the dissipation (death) of a random number of existing CPAs within the cyclonic system. The computer simulation, the results of which are presented in this paper, successfully reproduced the general mesoscale and synoptic scale features of the radar detected cyclonic rain fields as observed by Austin and Houze (1972), Houze et al. (1976), Hobbs (1978), Hobbs and Locatelli (1978), Houze (1981), Houze and Hobbs (1982) and others.     

Modeling long term lake variations by physically based stochastic dynamic models

Several physically based stochastic dynamic models (SDM) are described including year-to-year variations of water volume in terminal and non-terminal lakes, streamflow of lake-fed rivers, and salinity of an inland sea (the Sea of Azov). All of these models are based upon the SDM of water volume of terminal lakes developed by Kritzky and Menkel in 1946 in co-operation with Kolomogorov. Explicit formulae are derived for second order statistical moments of the output processes, including variance, correlation function, spectra, etc., under the assumption that the forcing functions from stationary random sequences. The least-squares prediction problem is solved for both stationary and non-stationary cases. Some of the processes are shown to possess high statistical predictability. Actual predictions are compared with independent observations. Problems for further study are stated.     

河流污染带的随机模拟方法

根据随机理论，推导了一个描述污染带变化的概率模型，并采用Ｍｏｎｔｅ－Ｃａｒｌｏ抽样法对其求数值解。该随机模型的解是一个随机物，实例计算表明，它的解能够反映任一计算点的浓度变化趋势及范围，并能够给浓度等值线附加上概率的意义，表现了在不确定因素的影响下，污染带随机变化的情况。     

Study of the crust and mantle using magnetic surveys by Magsat and other satellites

Among the first measurements made from near-Earth orbiting satellites were measurements of the magnetic field. The sources of that field lie both within the Earth, in its core and crust, and in the surrounding ionosphere and magnetosphere. This article summarizes some of the methodology and results for studies of the Earth’s mantle and crust. Mantle conductivity studies can be made either by studying signals impressed on the Earth from outside, e.g., the ionosphere or magnetosphere, or by studying signals originating in the core and transmitted through the mantle. Crustal field studies begin with a careful selection of the data and subsequent removal of core and external fields by some sort of filtering. Average maps from different local times sometimes differ, presumably due to the remaining presence of fields of external origin. Several techniques for further filtering are discussed. Where large-area aeromagnetic maps are available, crustal maps derived from satellite data can be compared with upward continued data. In general, the comparisons show agreement, with some differences, particularly in and near the auroral belts. The satellite data are further reduced by various methods of inverse and forward modelling, sometimes including reduction to the pole (RTP). These techniques are generally unstable at the equator. Common methods of stabilizing the inversions include principle components analysis and ridge regression. Because of the presence of the core field, the entire crustal contribution from the field is not known. Also, there is a basic nonuniqueness to the inverse solutions. Nevertheless, magnetizations that are interpretable can be derived.     

PRELIMINARY STUDY OF BAROTROPIC STOCHASTIC DIFFERENCE MODEL APPLIED TO WEATHER PREDICTION

In order to consider both the deterministic and the stochastic property of atmospheric motion simul-taneously,in this paper,the weather prediction is proposed as the problem of the evolution of meteorologicalfield.The historical viewpoint of atmospheric motion is emphasized here.Based on time series analysis te-chnique,a stochastic-dynamical model with multiple initial fields is derived.Thus,weather forecasting is sum-meal up as a problem of solving a set of stochastic difference equations.For the barotropic atmosphere,thenumerical solutions of the equations are obtained by using the method of empirical orthogonal functions(EOF),and examples of medium-range weather prediction are given here.Meanwhile,selecting the order oftime series,i.e.,determining the number of initial fields properly,is also discussed.     

Micro-scale modelling in the study of plume evolution in heterogeneous media

The migration of contaminants in heterogeneous aquifers involves dispersive processes that act at different scales. The interaction of these processes as a plume evolves can be studied by micro-scale modelling whereby two scales, a local- or micro-scale and an aquifer- or macro-scale, are covered simultaneously. Local-scale dispersive processes are represented through the local dispersion coefficient in the transport equation, while large-scale dispersion due to heterogeneities is represented through the resolution of the flow field and the diffusive exchange between streamtubes. The micro-scale model provides both the high degree of resolution compatible with local-scale processes, and the extent required for the approach to asymptotic conditions, using grids of up to a million nodal points. The model is based on the dual potential-streamfunction formulation for flow, and the transport problem is formulated in a natural coordinate system provided by the flownet. Simulations can be used to verify stochastic theories of dispersion, without the restrictive assumptions inherent in the theory. For the two-dimensional case, results indicate convergence of the effective dispersivity to the theoretical macrodispersivity value. Convergence takes place within a travel distance of about 50 correlation lengths of the hydraulic conductivity field. However, the approach taken to asymptotic conditions, as well as the macrodispersivity value, may differ for different realizations of the same medium. The influence of early-time events such as plume splitting on the asymptotic convergence remains to be investigated.